Question

Investment Example

An investor has $70,000 to divide among several instruments. Municipal bonds have an 8.5% return, C D’s a 5% return, t-bills a 6.5% return, and growth stock 13%. The following guidelines have been established:

-No more than 20% in municipal bonds

-Investment in C D s should not exceed the other three alternatives

-At least 30% invested in treasury bills and C D s

-More should be invested in C D s and treasury bills than in municipal bonds and growth stocks by a ratio of 1.2 to 1

-All $70,000 should be invested.

Write down your mathematical formulation.

Decision variables (10 points)

Objective function (5 points)

Constraints (Please label each constraint) (5 points)

Answer 1

An investor has total $70000 to invest.

Decision Variables:

Let investment in Municipal bonds = x1

Investment in CD = x2

Investment in treasury bills = x3

Investment in growth stocks = x4

Objective Function:

We have to maximize the return.

Return on Municipal bonds = 8.5%

Return on CDs = 5%

Return on treasury bills = 6.5%

Return on growth stock = 13%

Hence Objective function is: Maximize 0.085*x1 + 0.05*x2 + 0.065*x3 + 0.13*x4

Constraints:

No more than 20% in municipal bonds

x1 <= 14000 (Municipal Bonds)

Investment in CDs should not exceed the other three.

x2 <= x1 + x3 + x4

x2 – x1 – x3 – x4 <= 0 (Investment in CDs)

At least 30% invested in treasury bills and CDs

x2 + x3 >= 21000 (total of t-bills and CDs)

Total of CDs and treasury bills/total of municipal bonds and growth stocks >= 1.2/1

x2 + x3 >= 1.2*x1 + 1.2*x4

x2 -1.2*x1 + x3 – 1.2*x4 >= 0 (Investment ratio)

All $70000 should be used.

x1 + x2 + x3 + x4 = 70000 (Total Investment)

Hence the mathematical Formulation:

Decision Variables:

Let investment in Municipal bonds = x1

Investment in CD = x2

Investment in treasury bills = x3

Investment in growth stocks = x4

Objective Function:

Maximize 0.085*x1 + 0.05*x2 + 0.065*x3 + 0.13*x4

Constraints:

x1 <= 14000 (Municipal Bonds)

x2 – x1 – x3 – x4 <= 0 (Investment in CDs)

x2 + x3 >= 21000 (total of t-bills and CDs)

x2 -1.2*x1 + x3 – 1.2*x4 >= 0 (Investment ratio)

x1 + x2 + x3 + x4 = 70000 (Total Investment)

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